Rule: Q[4, 5]

Type

This rule is of Chebyshev U (second kind) type.

Polynomials

One starts from the polynomial $P_{1}$ and extends one by one with $P_{i}$ until the final polynomial defining this rule is reached.
Note: Polynomials might be truncated due to size! The complete polynomials are included in the download.

$P_{1}$ :
$16 \cdot t^{4} - 12 \cdot t^{2} + 1$
$P_{2}$ :
$16 \cdot t^{9} - 32 \cdot t^{7} + 21 \cdot t^{5} - 5 \cdot t^{3} + \frac{5}{16} \cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
0.95105651629515357212 + 5.299469827377980908e-169j	3.33e-62, 3.33e-62j
-0.58778525229247312917 + 1.324867456844495227e-169j	1.79e-62, 1.79e-62j
-0.95105651629515357212 - 1.5809074315074919812e-178j	4.4e-62, 4.4e-62j
0.3090169943749474241 + 2.8728483499322940323e-188j	3.46e-63, 3.46e-63j
0.8090169943749474241 - 6.5321008831513018601e-201j	4.13e-62, 4.13e-62j
0.58778525229247312917 + 5.9409111446723744485e-213j	1.79e-62, 1.79e-62j
-1.4504177599297789181e-216 - 1.8130221999122236476e-217j	1.32e-215, 1.32e-215j
-0.8090169943749474241 - 7.0821179684071236235e-220j	4.01e-62, 4.01e-62j
-0.3090169943749474241 + 0j	3.46e-63, 3.46e-63j

Weights

Weight (ball center)	Error (ball radius)
0.0095491502812526287949 - 7.4779294575573139878e-170j	1.51e-25, 5.26e-56j
0.065450849718747371205 - 1.0858928205333516645e-170j	6.13e-26, 2.13e-56j
0.0095491502812526287949 - 6.1431053287447903774e-171j	3.11e-26, 1.08e-56j
0.090450849718747371205 + 6.1296675760562513259e-170j	2.62e-26, 9.11e-57j
0.034549150281252628795 + 1.2562528984155116603e-169j	9.48e-27, 3.31e-57j
0.065450849718747371205 - 8.8104628084697396562e-170j	1.17e-26, 4.07e-57j
0.1 - 3.3181931873925397489e-170j	7.09e-27, 2.46e-57j
0.034549150281252628795 + 3.1092619536899008072e-170j	1.12e-27, 4.15e-58j
0.090450849718747371205 - 4.9466970707384464078e-171j	3.23e-27, 1.08e-57j

Download

All rules of Chebyshev U (second kind) type can be downloaded here packed into a single file.